Law of Sines

From NCTM "Illuminations".  Detailed lesson plan with student activity sheets. Students use right triangle geometry to develop the Law of Sines.  Includes options for assessment.  The ambiguous case is addressed in the "Extensions" section at the end of the lesson.  Would be nicely paired with the following interactive demo in GeoGebra:  http://www.mnwest.edu/fileadmin/static/website/dmatthews/Geogebra/LawOfS....  Students learn the law of sines, then use it to find missing side and angles. Lesson includes ambiguous case.

Weblink address (URL): 
Law of Sines

Standards & Objectives

Learning objectives: 

Students will:

  • Use right triangle trigonometry to develop the law of sines.
  • Use the law of sines to solve problems.
Essential and guiding questions: 
  • Given: ΔABC with m∠A = 79.39°, m∠B = 44.77°, and a = 7.07 cm. Is there a unique triangle with the following angle and side measures? Why?
  • If two angles and a non‑included side of a triangle are known, the law of sines can be used to determine the missing angle and sides. For what other combinations of angles and sides could the law of sines be used to determine the missing angles and sides of a triangle?
  • Of ASA and SSA, which guarantees a unique triangle? Why?

Lesson Variations

Blooms taxonomy level: 
Applying
Extension suggestions: 

An extension to this lesson is included in the material in the link.

Helpful Hints

The only material needed is provided through the site.

References

Contributors: 
Jennifer Bruce
Originator: 
Ayers Institute for Learning & Innovation